Question: Ishaan is 8 years older than Kevin. For the last four years, Ishaan and Kevin have been going to the same school. Five years ago, Ishaan was 3 times as old as Kevin. How old is Ishaan now?
Solution: We can use the given information to write down two equations that describe the ages of Ishaan and Kevin. Let Ishaan's current age be $i$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $i = k + 8$ Five years ago, Ishaan was $i - 5$ years old, and Kevin was $k - 5$ years old. The information in the second sentence can be expressed in the following equation: $i - 5 = 3(k - 5)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to solve our first equation for $k$ and substitute it into our second equation. Solving our first equation for $k$ , we get: $k = i - 8$ . Substituting this into our second equation, we get the equation: $i - 5 = 3($ $(i - 8)$ $ -$ $ 5)$ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 5 = 3i - 39$ Solving for $i$ , we get: $2 i = 34$ $i = 17$.